Matrices of linear forms of constant rank from vector bundles on projective spaces

2023/04/17 by Laurent Manivel, Manivel, Laurent, Rosa M. Miró‐Roig +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2304.08055

openalex publication_date 2023/04/17 · openalex created_date 2023/04/21 · openalex updated_date 2026/07/28

Abstract

We consider the problem of constructing matrices of linear forms of constant rank by focusing on the associated vector bundles on projective spaces. Important examples are given by the classical Steiner bundles, as well as some special (duals of) syzygy bundles that we call Drézet bundles. Using the classification of globally generated vector bundles with small first Chern class on projective spaces, we are able to describe completely the indecomposable matrices of constant rank up to six; some of them come from rigid homogeneous vector bundles, some other from Drézet bundles related either to plane quartics or to instanton bundles on the three-dimensional projective space.

Related

• Characterization of linear spaces of matrices of constant rank from syzygy bundles
• Equivariant spaces of matrices of constant rank
• Truncated modules and linear presentations of vector bundles
• Large rank simple bundles of all homological dimensions
• On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties